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The Econometrics Of The Eurozone’s CDS And Bond Spread

How The Model Works

The Econometrics Of The Eurozone’s CDS And Bond Spread

Antonello D’Agostino and Michael Ehrmann, the Senior Economist and the Directorate-General for research and economics at the ECB in 2010, stressed that understanding pricing mechanisms in sovereign debts markets were essential. Indeed, they argue in their paper that market’s sentiments towards a particular government bond could provoke either an overvaluation or an undervaluation of the bond. This feature concerns every country independently of its fiscal, monetary status (strong or weak), e.g. France losing its Standard and Poor’s AAA-rating back in January 2012.

Many kinds of literature proposed to relax the standards that had been commonly used to derive sovereign bond spreads. One can refer to the extensive use of relative variables (comparing a country’s macroeconomic figures to another country considered as a benchmark). Such practice set up strong hypotheses, namely that both countries’ data are equally relevant in order to explain the delta in the spread. Models, which allow fewer assumptions, lead to better results and are much more beneficial to one’s comprehension of pricing mechanisms. Due to this fact, examples that are presented within this article include regressors ranging from investors’ risk appetite to economic indicators and different sorts of measures used as proxies for markets’ volatility.

Modelling CDS And Bond Spread

Fontana and Scheirer, ECB’advisers in 2010, derived the following model in 2010:

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The equation 1 sets up a relationship between country i’s Credit Default Swap (where buyers of loans are compensated by the sellers in case of default) spread at time t (dependent variable) and a set of five distinguished explanatory variables using a usual panel regression: risk free rate, risk appetite (RA), corporate CDS premium, country’s public debt (Debt), idiosyncratic equity volatility (Vol) and bid-ask spread (Bid_Ask). The D’s are dummy variables for countries for which fiscal policy status is considered weak by the markets (Ireland, Portugal, Greece, Spain and Italy). Fontana and Scheirer include these variables in their initial model for their importance in the literature on credit spreads and their representation of markets’ sentiment. These variables include;

  1. The risk free rate (Euribor three-month short rate) that is negatively correlated with credit spread according to the Merton model (1974)
  2. RA and iTraxx that represent both investors’ risk appetite towards markets (iTraxx is a proxy for credit risk appetite, while RA is a proxy for the overall risk appetite)
  3. Macroeconomic fundamentals captured by Debt and markets environment pictured by their liquidity (Bid-Ask spread) and their Volatility (Vol) that both increases the change in credit spread.

Equation 1 is derived for country’s bond spread ceteris paribus.

The results of the panel regression are reported in Table 1 and Table 2, respectively for the CDS spread and the bond spread.


Figure 1: Panel regression outputs for CDS spread


Figure 2: Panel regression outputs for bond spread

As it can be depicted in Table 1 and Table 2, the panel regressions were run on a dataset subdivided into samples: the first part (PI) covers the period from 2 January 2006 to 8 September 2008 (ante financial crisis) and the second part (PII) ranges from 15 September 2008 to June 2010 (post financial crisis and ante-European debt crisis).

Fontana and Scheirer inferred several conclusions from those outputs:

  • Macroeconomic variable (Debt) is significant to explain the bond spread in the second subsample, whereas it does not affect CDS spread at all.
  • Investors’ risk appetite is statistically relevant and is positively correlated with CDS spread of dummy variables in the second sub-period.
  • DiTraxx and iTraxx are always significant. Ergo, the credit market is a primordial factor for both dependent variables and particularly for Greece, Italy, Spain, Ireland and Portugal (iTraxx < DiTraxx). As a matter of fact, the credit market is a major component in pricing CDS and sovereign bonds.

Those observations lead Fontana and Scheirer to perform further analyses of the phenomena they observed. Therefore, they switched their initial set of variables before investigating on series cointegration. The list of new regressors is given as follows: Euro OverNight Index Average (EONIA), Implied volatility index (VIX), Idiosyncratic equity return (R), Slope of term structure (SLOPE) and Exchange rate uncertainty (USDVOL). Vol and Debt were kept within the second regression. EONIA is a different proxy for short rate. The significance of VIX for sovereign credit risk was shown by Pan and Singleton (2007) and replaces iTraxx and RA.

R is meant to represent country’s economic state, thus is expected to lower country’s spreads. SLOPE is the difference between the ten-year euro swap rate and the three-month Euribor rate. Due to the negative correlation between SLOPE and credit spread as derived by Longstaff and Schwarz, country’s spreads are expected to decrease as SLOPE rises. The increase of USDVOL should be mirrored in an increase independent variables. The aforementioned regressor reflects the fact that contracts are denominated in US dollars. The same group of dummies (D) present in equation (1) is part of the second regression.

The second equation summarising Fontana and Scheirer’s findings is given below:

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Figure 3: Provides the output of the regression.

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Figure 4: Extended regression model (Source: ECB)

In Figure 3, the ECB’s advisers focused solely on the second period given that market pricing was less linked to fundamentals in equation 1. Some regressors’ significance confirms Fontana and Scheirer’s hypotheses. Indeed, SLOPE is relevant for both dependent variables and has got roughly the same impact. The CDS spread of Greece, Italy, Portugal, Spain and Ireland is affected by USD_VOL, while the other sample members are not.

Surprisingly, R does not have any influence. This irrelevance could be caused by the fact that national stock exchanges in Europe are all linked to Euronext and hence any potential effects of R is cancelled out.

As the last step of their research, they measured the adjustment process between the dependent variable. A vector equilibrium correction model (VECM) was used to complete that task. VECM allows one to analyse how two cointegrated series behave in the long run. The Augmented Dickey-Fuller test (ADF) was applied on the ten series, and it turned out that the series were integrated once. The dynamics of CDS and bond spread changes in the short term are derived by equations 3 and 4, whereas equation 5 is the long run equation describing deviations of CDS and yield spreads:

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Figure 5: Dynamics of CDS vs Spreads

The results of the cointegration analysis are reported in Figure 6.

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Figure 6: Results of the cointegration analysis


Figure 6 provides the outcome of the test only for the second subsample. Fontana and Scheirer drew a relevant conclusion that tends to confirm the hypothesis suggested by D’Agostino and Ehrmann.

The explanatory variable (negative) is not rejected by Germany, France, the Netherlands, Austria and Belgium, but it is statistically insignificant for Greece, Portugal, Ireland, Spain and Italy. Concerning the story is the exact opposite. These facts mean that the determination of the spot price takes place in the cash market for the first group of countries, while the derivatives market sets the tone for the second one.

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